Statistical inference from a single sample of data
Statistical inference from multiple samples of data
The only way to reduce both types of error is to collect more evidence or, in statistical terms, to collect more data.
\(\alpha = Pr(\text{Type I error})\): If \(H_0\) is true, this is the probability that we (incorrectly) reject it.
\(\beta = Pr(\text{Type II error})\): If \(H_0\) is false, this is the probability that we (incorrectly) fail to reject it.
\(1-\beta = Power\) If \(H_0\) is false, this is the probability that we (correctly) reject it.
On average, how much more money do consumers spend at Target compared to Walmart?
Suppose researchers collected a systematic sample from \(85\) Walmart customers and \(80\) Target customers by asking them for their purchase amount as they left the stores. The data they collected is summarized in the table below. Suppose a computer already calculated the degrees of freedom to be \(162.75\).
| Walmart | Target | |
|---|---|---|
| \(\bar{x}\) | \(\$45\) | \(\$53\) |
| s | \(\$21\) | \(\$19\) |
Step 1) Identify and define the population parameter and choose your confidence level.
Step 2) Calculate the sample estimate for the population parameter.
Step 3) Assess the required assumptions and conditions.
Step 4) Find the critical value corresponding to your confidence level.
Step 5) Calculate the standard error of your sample estimate.
Step 6) Calculate the lower and upper bounds of your confidence interval.
On average, how large is the difference in car insurance prices for customers of an online insurance company versus customers of a local insurance company?
Find a \(95\%\) confidence interval for the mean difference in insurance prices based on the data given below.
mean(insurance_diff$PriceDiff)
## [1] 45.9
sd(insurance_diff$PriceDiff)
## [1] 175.6628
t.test(insurance_diff$PriceDiff, mu=0, conf.level=0.95)
##
## One Sample t-test
##
## data: insurance_diff$PriceDiff
## t = 0.82629, df = 9, p-value = 0.43
## alternative hypothesis: true mean is not equal to 0
## 95 percent confidence interval:
## -79.76163 171.56163
## sample estimates:
## mean of x
## 45.9
Week 14 - new statistical method (our last one for the semester)
Week 14 and 15 - begin discussions on ethical statistical practice
Week 15 - Friday in-class poster presentation
You and your group mates are welcome to attend anytime between 9:30am-10:30am or 11:00am-12:30pm.
Plan to spend at least 45 minutes in class and come early to hang up your poster in the room. (Prof Suzy will provide hanging supplies.)
Prof Suzy will take turns meeting with each group for 5-7 minutes where you will present your topic.
All participants will be asked to take some time and read the other posters. Each person will need to submit a 3-4 sentence summary ion another group’s project in order to get credit for attendance this day.